Block #2,237,247

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/4/2017, 11:19:01 PM · Difficulty 10.9462 · 4,589,074 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d78f3f33678caa0d1d2c5b9e758d5d2dd8eb78450a198925bce960158b0ca083

View on Chainz ↗

Height

#2,237,247

Difficulty

10.946165

Transactions

Size

2.05 KB

Version

Bits

0af237e3

Nonce

482,484,346

Timestamp

8/4/2017, 11:19:01 PM

Confirmations

4,589,074

Mined by

⛏️ P2SHAaRPNiaBtHxrrdYE4WZGFUjF8uCfHa8AVM

Merkle Root

1eb1bbd4b5b4f7af90799e5b36fcdc5621475e292139ea8019d4f3a5558a1c63

Transactions (5)

Coinbase88901422317d93…beaa22bb56a3e5

1 in → 1 out8.3700 XPM109 B

AaRPNiaB…CfHa8AVM

1a9ea60b2ae7b5…deb67665e73efb

4 in → 2 out1483.0552 XPM671 B

AWRDnK93…19Vviqfz AdnGP8Jv…YfPbjJc8

b50f7825669559…309888b1281131

2 in → 2 out10.4769 XPM339 B

AJ21tfPP…k3r8ZHsm AYiVkR5s…Waom7bcN

686805e204616d…18e57118da0566

1 in → 2 out7.2014 XPM226 B

Ad7P1LFX…wYEh2Qob AQEfWikv…AFFvFEyz

ae9ad8cd694245…22448b19b830d1

4 in → 2 out4.1048 XPM668 B

ASdXKexa…kch59HW5 AaCscfdU…d8w69csr

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.

1.484 × 10⁹⁸(99-digit number)

14843189414252178648…60652841341665279999

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

1.484 × 10⁹⁸(99-digit number)

14843189414252178648…60652841341665279999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.484 × 10⁹⁸(99-digit number)

14843189414252178648…60652841341665280001

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

2.968 × 10⁹⁸(99-digit number)

29686378828504357296…21305682683330559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.968 × 10⁹⁸(99-digit number)

29686378828504357296…21305682683330560001

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

5.937 × 10⁹⁸(99-digit number)

59372757657008714592…42611365366661119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.937 × 10⁹⁸(99-digit number)

59372757657008714592…42611365366661120001

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

1.187 × 10⁹⁹(100-digit number)

11874551531401742918…85222730733322239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.187 × 10⁹⁹(100-digit number)

11874551531401742918…85222730733322240001

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

2.374 × 10⁹⁹(100-digit number)

23749103062803485836…70445461466644479999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.374 × 10⁹⁹(100-digit number)

23749103062803485836…70445461466644480001

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 #2,237,247

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