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Block #234,716

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2013, 12:08:10 PM Β· Difficulty 9.9445 Β· 6,572,474 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
76ea0ae02bf3e207b469562855592643de7aa8172cfc7048b0d2f335ff4226f3
View on Chainz β†—

Height

#234,716

Difficulty

9.944450

Transactions

1

Size

206 B

Version

2

Bits

09f1c77a

Nonce

189,335

Timestamp

10/30/2013, 12:08:10 PM

Confirmations

6,572,474

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

f7770ba43615fe842bf52f602d125857dec9f9e4a67d880729f8f6322b3af766
Transactions (1)
Coinbasef7770ba43615fe…f8f6322b3af766
1 in β†’ 1 out10.1000 XPM116 B
AcLBm5Z9…S683d7c3
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.

9.737 Γ— 10⁹³(94-digit number)
97379107983006865185…02270655092113504159
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
9.737 Γ— 10⁹³(94-digit number)
97379107983006865185…02270655092113504159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.737 Γ— 10⁹³(94-digit number)
97379107983006865185…02270655092113504161
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
1.947 Γ— 10⁹⁴(95-digit number)
19475821596601373037…04541310184227008319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.947 Γ— 10⁹⁴(95-digit number)
19475821596601373037…04541310184227008321
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
3.895 Γ— 10⁹⁴(95-digit number)
38951643193202746074…09082620368454016639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.895 Γ— 10⁹⁴(95-digit number)
38951643193202746074…09082620368454016641
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
7.790 Γ— 10⁹⁴(95-digit number)
77903286386405492148…18165240736908033279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.790 Γ— 10⁹⁴(95-digit number)
77903286386405492148…18165240736908033281
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
1.558 Γ— 10⁹⁡(96-digit number)
15580657277281098429…36330481473816066559
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,701,532 XPMΒ·at block #6,807,189 Β· updates every 60s
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