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Block #51,674

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 6:51:57 AM Β· Difficulty 8.9018 Β· 6,756,757 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7b8c487e78ef7c14f24de7f197cafb27d4970c735b5e1333f7f64ac65cd0a7b3
View on Chainz β†—

Height

#51,674

Difficulty

8.901835

Transactions

1

Size

203 B

Version

2

Bits

08e6dea6

Nonce

293

Timestamp

7/16/2013, 6:51:57 AM

Confirmations

6,756,757

Merkle Root

7c4496b4b2ddd727a1080a52feac3e4997201d6bc1dcdb966878185ff20708b0
Transactions (1)
Coinbase7c4496b4b2ddd7…78185ff20708b0
1 in β†’ 1 out12.6000 XPM109 B
AZL9DFFi…mwQY3vsF
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.

9.979 Γ— 10¹⁰⁴(105-digit number)
99795400628228538068…19150774636893419800
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
9.979 Γ— 10¹⁰⁴(105-digit number)
99795400628228538068…19150774636893419799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.979 Γ— 10¹⁰⁴(105-digit number)
99795400628228538068…19150774636893419801
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
1.995 Γ— 10¹⁰⁡(106-digit number)
19959080125645707613…38301549273786839599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.995 Γ— 10¹⁰⁡(106-digit number)
19959080125645707613…38301549273786839601
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
3.991 Γ— 10¹⁰⁡(106-digit number)
39918160251291415227…76603098547573679199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.991 Γ— 10¹⁰⁡(106-digit number)
39918160251291415227…76603098547573679201
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
7.983 Γ— 10¹⁰⁡(106-digit number)
79836320502582830455…53206197095147358399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.983 Γ— 10¹⁰⁡(106-digit number)
79836320502582830455…53206197095147358401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8
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 51674

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 7b8c487e78ef7c14f24de7f197cafb27d4970c735b5e1333f7f64ac65cd0a7b3

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 #51,674 on Chainz β†—
Circulating Supply:57,711,509 XPMΒ·at block #6,808,430 Β· updates every 60s
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