Block #260,614

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/14/2013, 12:36:16 PM · Difficulty 9.9769 · 6,554,334 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e77ab5e2fc8e867222a3db83c763a29af35212e8cfd7aa16da87f599c550772

View on Chainz ↗

Height

#260,614

Difficulty

9.976856

Transactions

Size

685 B

Version

Bits

09fa133b

Nonce

87,520

Timestamp

11/14/2013, 12:36:16 PM

Confirmations

6,554,334

Mined by

⛏️ P2SHANM955wqRacWtzReCt4mwUWpPCwGTsHjnv

Merkle Root

ef083a30c7ec4f3a1e024c3225e18990f89e1563ae09b99f3644978a274534f2

Transactions (3)

Coinbase0a2ec5deb8c968…1c3818e71e36a0

1 in → 1 out10.0500 XPM109 B

ANM955wq…wGTsHjnv

8c69d3659bc9da…9a46dc81e904ab

1 in → 4 out10.0200 XPM260 B

AJPry4G9…ost1kKHz AeKNrjNj…1NEq95Ta AGQ2fgRV…bLy3QAAV AUHFmvnF…juaRoiLd

1e0add0645a1f8…fd9989a9619c07

1 in → 2 out21.6211 XPM226 B

AG4HJkPC…N9wjLQmz AaKj4FrX…gTv9wa4L

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.

1.137 × 10⁹⁵(96-digit number)

11379692434381760121…30811538668553225909

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

1.137 × 10⁹⁵(96-digit number)

11379692434381760121…30811538668553225909

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.137 × 10⁹⁵(96-digit number)

11379692434381760121…30811538668553225911

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

2.275 × 10⁹⁵(96-digit number)

22759384868763520242…61623077337106451819

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.275 × 10⁹⁵(96-digit number)

22759384868763520242…61623077337106451821

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

4.551 × 10⁹⁵(96-digit number)

45518769737527040485…23246154674212903639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.551 × 10⁹⁵(96-digit number)

45518769737527040485…23246154674212903641

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

9.103 × 10⁹⁵(96-digit number)

91037539475054080971…46492309348425807279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.103 × 10⁹⁵(96-digit number)

91037539475054080971…46492309348425807281

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

1.820 × 10⁹⁶(97-digit number)

18207507895010816194…92984618696851614559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.820 × 10⁹⁶(97-digit number)

18207507895010816194…92984618696851614561

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 #260,614

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