Block #2,127,573

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/22/2017, 2:23:54 AM · Difficulty 10.9181 · 4,704,065 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

024dd48e2c8b6d2fa81dcf3dfa65dc4a245fc28c0c295f39235d4476fd910eaf

View on Chainz ↗

Height

#2,127,573

Difficulty

10.918082

Transactions

Size

653 B

Version

Bits

0aeb0773

Nonce

50,285,949

Timestamp

5/22/2017, 2:23:54 AM

Confirmations

4,704,065

Mined by

⛏️ P2SHAe8ZMhk1rWbSVmhJo6NLvJaSaAr1JSmBvq

Merkle Root

90963301d1c76bddf695917b7a3fd3525e8a52e5b4c6ecbd809baca9b4399f07

Transactions (3)

Coinbase6f81a1a1f47ab1…86e4f4d420c713

1 in → 1 out8.4000 XPM110 B

Ae8ZMhk1…r1JSmBvq

40376f300457f1…75f9946bd10bf4

1 in → 2 out198511.1753 XPM227 B

ATNNwPCV…id21vw5x AP5baBjj…H5WqTjxq

55593f74dbf0cd…c03d4b817f773f

1 in → 2 out186609.3853 XPM225 B

AeHoLpMz…atD1PEUN Ad9ogDF1…SNfvDzrq

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.

2.434 × 10⁹⁶(97-digit number)

24341792436070378473…43150910580958167039

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

2.434 × 10⁹⁶(97-digit number)

24341792436070378473…43150910580958167039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.434 × 10⁹⁶(97-digit number)

24341792436070378473…43150910580958167041

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

4.868 × 10⁹⁶(97-digit number)

48683584872140756946…86301821161916334079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.868 × 10⁹⁶(97-digit number)

48683584872140756946…86301821161916334081

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

9.736 × 10⁹⁶(97-digit number)

97367169744281513892…72603642323832668159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.736 × 10⁹⁶(97-digit number)

97367169744281513892…72603642323832668161

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

1.947 × 10⁹⁷(98-digit number)

19473433948856302778…45207284647665336319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.947 × 10⁹⁷(98-digit number)

19473433948856302778…45207284647665336321

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

3.894 × 10⁹⁷(98-digit number)

38946867897712605556…90414569295330672639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.894 × 10⁹⁷(98-digit number)

38946867897712605556…90414569295330672641

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 #2,127,573

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