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Block #60,015

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 5:32:52 AM Β· Difficulty 8.9675 Β· 6,756,792 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1cea9090cbdb706ef0fa8351173a8a6acd3a438bd537fa56d4bfcbb0683537eb
View on Chainz β†—

Height

#60,015

Difficulty

8.967455

Transactions

1

Size

205 B

Version

2

Bits

08f7ab1d

Nonce

253

Timestamp

7/18/2013, 5:32:52 AM

Confirmations

6,756,792

Merkle Root

6f56211a81c6d75c78860ec48ebfb19554d869d072a8e59cf936f7ca433a093a
Transactions (1)
Coinbase6f56211a81c6d7…36f7ca433a093a
1 in β†’ 1 out12.4200 XPM110 B
AU1wVv6L…XQP85YX2
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.

1.125 Γ— 10¹⁰⁢(107-digit number)
11256564326619491188…73701696309395924080
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
1.125 Γ— 10¹⁰⁢(107-digit number)
11256564326619491188…73701696309395924079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.125 Γ— 10¹⁰⁢(107-digit number)
11256564326619491188…73701696309395924081
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
2.251 Γ— 10¹⁰⁢(107-digit number)
22513128653238982376…47403392618791848159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.251 Γ— 10¹⁰⁢(107-digit number)
22513128653238982376…47403392618791848161
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
4.502 Γ— 10¹⁰⁢(107-digit number)
45026257306477964752…94806785237583696319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.502 Γ— 10¹⁰⁢(107-digit number)
45026257306477964752…94806785237583696321
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
9.005 Γ— 10¹⁰⁢(107-digit number)
90052514612955929505…89613570475167392639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.005 Γ— 10¹⁰⁢(107-digit number)
90052514612955929505…89613570475167392641
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
1.801 Γ— 10¹⁰⁷(108-digit number)
18010502922591185901…79227140950334785279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 60015

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 1cea9090cbdb706ef0fa8351173a8a6acd3a438bd537fa56d4bfcbb0683537eb

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 #60,015 on Chainz β†—
Circulating Supply:57,778,493 XPMΒ·at block #6,816,806 Β· updates every 60s
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