Block #1,484,738

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/5/2016, 12:06:42 PM · Difficulty 10.7290 · 5,342,266 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b37efd60401945b8071be149388ab6af936a4306a077c6e212f7a855bb82e06a

View on Chainz ↗

Height

#1,484,738

Difficulty

10.728952

Transactions

Size

6.59 KB

Version

Bits

0aba9c99

Nonce

1,901,466,992

Timestamp

3/5/2016, 12:06:42 PM

Confirmations

5,342,266

Mined by

⛏️ P2SHAJEkrMqegperCNMw4n7i7w7SFHQhwHsvaE

Merkle Root

86bd61238e06733dae4624b37b750c90c98654edb9618fdfb6995ef72c9174d8

Transactions (4)

Coinbase60c366c3890e0f…9b39d643101888

1 in → 1 out8.7500 XPM109 B

AJEkrMqe…QhwHsvaE

584d26eeb6783e…03f772e609b33d

5 in → 2 out19.9900 XPM816 B

AYndQcTj…o2TCngrN AJWhq16D…FE6LaN8E

326572a799b735…1aa20a7b90309a

31 in → 2 out46.4041 XPM4.55 KB

AHNkwmbJ…EUxEmniY AemRzd4d…aEEszDyy

69d5ceca8e2b56…888dc3698d3cbd

1 in → 27 out107.9260 XPM1.05 KB

ATPM8K5Q…dSNeQYZV APjme5xC…2FVowiaD ANx381rY…1xevqKwn AZf9W1JN…qszfTtrK AYqkP9H7…2Gp2G7WX

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.

2.111 × 10⁹⁶(97-digit number)

21115086746823413776…13631850777640202239

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

2.111 × 10⁹⁶(97-digit number)

21115086746823413776…13631850777640202239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.111 × 10⁹⁶(97-digit number)

21115086746823413776…13631850777640202241

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

4.223 × 10⁹⁶(97-digit number)

42230173493646827552…27263701555280404479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.223 × 10⁹⁶(97-digit number)

42230173493646827552…27263701555280404481

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

8.446 × 10⁹⁶(97-digit number)

84460346987293655105…54527403110560808959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.446 × 10⁹⁶(97-digit number)

84460346987293655105…54527403110560808961

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

1.689 × 10⁹⁷(98-digit number)

16892069397458731021…09054806221121617919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.689 × 10⁹⁷(98-digit number)

16892069397458731021…09054806221121617921

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

3.378 × 10⁹⁷(98-digit number)

33784138794917462042…18109612442243235839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.378 × 10⁹⁷(98-digit number)

33784138794917462042…18109612442243235841

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

6.756 × 10⁹⁷(98-digit number)

67568277589834924084…36219224884486471679

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 #1,484,738

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