Block #2,147,141

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/5/2017, 3:47:14 PM · Difficulty 10.8926 · 4,689,760 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b989d0200cba6c54be9dace909cf81122a6367c115d37e23aef04c8ffb6e54fe

View on Chainz ↗

Height

#2,147,141

Difficulty

10.892585

Transactions

Size

1.14 KB

Version

Bits

0ae48078

Nonce

785,489,095

Timestamp

6/5/2017, 3:47:14 PM

Confirmations

4,689,760

Mined by

⛏️ P2SHASTDtwoP5sM2tisJAwgejoiYzR1Uh3dmxX

Merkle Root

a652fa20be47924a64dd0d79d2ae0b016deee04b996704148ed6217210c725ae

Transactions (2)

Coinbase6bf1b63fa9076c…5e26f4ad419b80

1 in → 1 out8.4200 XPM109 B

ASTDtwoP…1Uh3dmxX

b8cfcfa9446d07…da1923d7996318

6 in → 2 out990.0145 XPM965 B

AXFzqv7y…nYiWJYQC AM5iAcHi…EaSLASCq

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.

1.547 × 10⁹⁸(99-digit number)

15479530813520950697…77077493606707199999

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

1.547 × 10⁹⁸(99-digit number)

15479530813520950697…77077493606707199999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.547 × 10⁹⁸(99-digit number)

15479530813520950697…77077493606707200001

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

3.095 × 10⁹⁸(99-digit number)

30959061627041901394…54154987213414399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.095 × 10⁹⁸(99-digit number)

30959061627041901394…54154987213414400001

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

6.191 × 10⁹⁸(99-digit number)

61918123254083802789…08309974426828799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.191 × 10⁹⁸(99-digit number)

61918123254083802789…08309974426828800001

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

1.238 × 10⁹⁹(100-digit number)

12383624650816760557…16619948853657599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.238 × 10⁹⁹(100-digit number)

12383624650816760557…16619948853657600001

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

2.476 × 10⁹⁹(100-digit number)

24767249301633521115…33239897707315199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.476 × 10⁹⁹(100-digit number)

24767249301633521115…33239897707315200001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.953 × 10⁹⁹(100-digit number)

49534498603267042231…66479795414630399999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,147,141

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