Block #549,436

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/17/2014, 1:44:42 PM · Difficulty 10.9608 · 6,263,200 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cffa455d5db2ca4f1c6f3862766fcf4a7f097253002212e17ea09f84da296761

View on Chainz ↗

Height

#549,436

Difficulty

10.960754

Transactions

Size

1.23 KB

Version

Bits

0af5f3f3

Nonce

36,164,799

Timestamp

5/17/2014, 1:44:42 PM

Confirmations

6,263,200

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

970a3e50b624edafbc0e23161569ccafc0805a75defa2a44e56a1c8519551596

Transactions (5)

Coinbasee591eda8189925…149aeb307263be

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

82d26e8ac70865…b938f1389c94f9

1 in → 2 out7.1480 XPM227 B

AZLTumeb…6bST1Ezk AMTQjUNt…3VoRstBw

b87c0c4f702fa9…7b565ba3b431f1

1 in → 2 out7.0701 XPM226 B

AMkxEE5g…p4Dc46YA AYziGDCW…XJ5VxbsR

c36d3f33664c9e…d3b7da7ab90812

1 in → 2 out2.0620 XPM226 B

AS9ZCvju…bu3NEFwZ AY5MtD1w…EmvmqffD

61c9fe7551fcb4…5321fe7887e827

2 in → 2 out5.5922 XPM375 B

AenGiSGP…VmaExxbt Ac1CjmFL…7Et3tsz6

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.

2.679 × 10¹⁰⁰(101-digit number)

26792326889818566839…41092084319595379199

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

2.679 × 10¹⁰⁰(101-digit number)

26792326889818566839…41092084319595379199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.679 × 10¹⁰⁰(101-digit number)

26792326889818566839…41092084319595379201

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

5.358 × 10¹⁰⁰(101-digit number)

53584653779637133679…82184168639190758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.358 × 10¹⁰⁰(101-digit number)

53584653779637133679…82184168639190758401

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

1.071 × 10¹⁰¹(102-digit number)

10716930755927426735…64368337278381516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.071 × 10¹⁰¹(102-digit number)

10716930755927426735…64368337278381516801

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

2.143 × 10¹⁰¹(102-digit number)

21433861511854853471…28736674556763033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.143 × 10¹⁰¹(102-digit number)

21433861511854853471…28736674556763033601

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

4.286 × 10¹⁰¹(102-digit number)

42867723023709706943…57473349113526067199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.286 × 10¹⁰¹(102-digit number)

42867723023709706943…57473349113526067201

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

8.573 × 10¹⁰¹(102-digit number)

85735446047419413887…14946698227052134399

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 #549,436

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