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Block #236,032

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/31/2013, 6:50:36 AM Β· Difficulty 9.9466 Β· 6,560,857 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c872ec2aac88b57e3313b3f1153c623f6ad07679c2cede0d784b7902b8362dec
View on Chainz β†—

Height

#236,032

Difficulty

9.946573

Transactions

1

Size

200 B

Version

2

Bits

09f252a4

Nonce

375,977

Timestamp

10/31/2013, 6:50:36 AM

Confirmations

6,560,857

Mined by

⛏️ P2SHASUtGRx8bDVJURUf8WLJkL5tX6vh2tTKJs

Merkle Root

6370edc1b793fb7ec10a8f73df502259dffde20fc7298482857513cc4d60e145
Transactions (1)
Coinbase6370edc1b793fb…7513cc4d60e145
1 in β†’ 1 out10.0900 XPM109 B
ASUtGRx8…vh2tTKJs
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.

9.944 Γ— 10⁹⁡(96-digit number)
99440235580271035427…38099166746463265599
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
9.944 Γ— 10⁹⁡(96-digit number)
99440235580271035427…38099166746463265599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.944 Γ— 10⁹⁡(96-digit number)
99440235580271035427…38099166746463265601
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
1.988 Γ— 10⁹⁢(97-digit number)
19888047116054207085…76198333492926531199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.988 Γ— 10⁹⁢(97-digit number)
19888047116054207085…76198333492926531201
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
3.977 Γ— 10⁹⁢(97-digit number)
39776094232108414171…52396666985853062399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.977 Γ— 10⁹⁢(97-digit number)
39776094232108414171…52396666985853062401
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
7.955 Γ— 10⁹⁢(97-digit number)
79552188464216828342…04793333971706124799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.955 Γ— 10⁹⁢(97-digit number)
79552188464216828342…04793333971706124801
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
1.591 Γ— 10⁹⁷(98-digit number)
15910437692843365668…09586667943412249599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.591 Γ— 10⁹⁷(98-digit number)
15910437692843365668…09586667943412249601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,619,130 XPMΒ·at block #6,796,888 Β· updates every 60s
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