Block #623,917

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/8/2014, 6:36:07 PM · Difficulty 10.9573 · 6,186,734 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95acd0015bd4a83b4914552caa2d21692c6f533efcecdb400d475a6d4e04583e

View on Chainz ↗

Height

#623,917

Difficulty

10.957329

Transactions

Size

21.42 KB

Version

Bits

0af5137d

Nonce

695,292,325

Timestamp

7/8/2014, 6:36:07 PM

Confirmations

6,186,734

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9a723af8f93fcd1e15e363553a1e0627b242ebf1c575e4f16debffeaff4ab820

Transactions (3)

Coinbased7b0a73749ce74…eb9e17666151ca

1 in → 1 out8.5500 XPM116 B

ANSXnLY2…Sd25TjkD

cf969cae799e30…5edecab3004014

97 in → 301 out810.6199 XPM20.85 KB

AYHS4Nva…HBn5Ucv8 AXqd93yV…nKgMCPjv Abw9qcHX…3tovmw3w AWJoHvRV…kBmXc95w AeKwPJ8W…tPXUCjD9

01a7a6d43d1c49…264c608e865afe

2 in → 2 out5.3678 XPM374 B

AaDeSUf2…EZYQVAko AXiN448S…vbShp5d5

Prime Chain Origin

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

2.045 × 10⁹⁷(98-digit number)

20458257128404502196…55869388604138757119

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

2.045 × 10⁹⁷(98-digit number)

20458257128404502196…55869388604138757119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.045 × 10⁹⁷(98-digit number)

20458257128404502196…55869388604138757121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.091 × 10⁹⁷(98-digit number)

40916514256809004393…11738777208277514239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.091 × 10⁹⁷(98-digit number)

40916514256809004393…11738777208277514241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.183 × 10⁹⁷(98-digit number)

81833028513618008787…23477554416555028479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.183 × 10⁹⁷(98-digit number)

81833028513618008787…23477554416555028481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.636 × 10⁹⁸(99-digit number)

16366605702723601757…46955108833110056959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.636 × 10⁹⁸(99-digit number)

16366605702723601757…46955108833110056961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.273 × 10⁹⁸(99-digit number)

32733211405447203514…93910217666220113919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.273 × 10⁹⁸(99-digit number)

32733211405447203514…93910217666220113921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #623,917

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