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Block #867,655

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/25/2014, 11:07:20 AM Β· Difficulty 10.9626 Β· 5,957,150 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
056733b689c0556973e46aa380d590cf2ca2dcfbe7f61fa99d939fd099f6a9a3
View on Chainz β†—

Height

#867,655

Difficulty

10.962619

Transactions

1

Size

207 B

Version

2

Bits

0af66e30

Nonce

79,325,328

Timestamp

12/25/2014, 11:07:20 AM

Confirmations

5,957,150

Merkle Root

0be868c1925e944e038023a1be868890d9abc6525525b78e28ff554502651344
Transactions (1)
Coinbase0be868c1925e94…ff554502651344
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.615 Γ— 10⁹⁢(97-digit number)
36154445051800874918…21765228173857576960
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.615 Γ— 10⁹⁢(97-digit number)
36154445051800874918…21765228173857576959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.615 Γ— 10⁹⁢(97-digit number)
36154445051800874918…21765228173857576961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
7.230 Γ— 10⁹⁢(97-digit number)
72308890103601749836…43530456347715153919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.230 Γ— 10⁹⁢(97-digit number)
72308890103601749836…43530456347715153921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.446 Γ— 10⁹⁷(98-digit number)
14461778020720349967…87060912695430307839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.446 Γ— 10⁹⁷(98-digit number)
14461778020720349967…87060912695430307841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.892 Γ— 10⁹⁷(98-digit number)
28923556041440699934…74121825390860615679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.892 Γ— 10⁹⁷(98-digit number)
28923556041440699934…74121825390860615681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
5.784 Γ— 10⁹⁷(98-digit number)
57847112082881399869…48243650781721231359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.784 Γ— 10⁹⁷(98-digit number)
57847112082881399869…48243650781721231361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.156 Γ— 10⁹⁸(99-digit number)
11569422416576279973…96487301563442462719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 867655

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 056733b689c0556973e46aa380d590cf2ca2dcfbe7f61fa99d939fd099f6a9a3

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #867,655 on Chainz β†—
Circulating Supply:57,842,516 XPMΒ·at block #6,824,804 Β· updates every 60s
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