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Block #65,260

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2013, 11:25:52 AM Β· Difficulty 8.9837 Β· 6,729,882 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a361874f389288dcd8367f6d824ccc1054e2d42c01a058007c0484f4792f4238
View on Chainz β†—

Height

#65,260

Difficulty

8.983715

Transactions

3

Size

634 B

Version

2

Bits

08fbd4be

Nonce

24

Timestamp

7/19/2013, 11:25:52 AM

Confirmations

6,729,882

Mined by

⛏️ P2SHAMQ1QFypXuE4kTU7BnFRFKWDhv3r8FbPbA

Merkle Root

0ec736815e34d658808597cba0ca6aedcedfe7cc0509c9b03ffb8b78ac3910d7
Transactions (3)
Coinbase67ed8c39a70911…72ac2ebba207f6
1 in β†’ 1 out12.3900 XPM110 B
AMQ1QFyp…3r8FbPbA
c4bb10e6b1dcf0…fc181f45bd1018
2 in β†’ 1 out24.8800 XPM273 B
AFtap2en…4d4n6Nrg
b066b5a965d931…4d7becea3b342d
1 in β†’ 1 out12.3900 XPM159 B
Ad3hHLDx…mq8Afkvv
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.040 Γ— 10⁹⁹(100-digit number)
20406220974698948369…07401791369358155079
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.040 Γ— 10⁹⁹(100-digit number)
20406220974698948369…07401791369358155079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.040 Γ— 10⁹⁹(100-digit number)
20406220974698948369…07401791369358155081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.081 Γ— 10⁹⁹(100-digit number)
40812441949397896739…14803582738716310159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.081 Γ— 10⁹⁹(100-digit number)
40812441949397896739…14803582738716310161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
8.162 Γ— 10⁹⁹(100-digit number)
81624883898795793478…29607165477432620319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.162 Γ— 10⁹⁹(100-digit number)
81624883898795793478…29607165477432620321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.632 Γ— 10¹⁰⁰(101-digit number)
16324976779759158695…59214330954865240639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.632 Γ— 10¹⁰⁰(101-digit number)
16324976779759158695…59214330954865240641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.264 Γ— 10¹⁰⁰(101-digit number)
32649953559518317391…18428661909730481279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,605,177 XPMΒ·at block #6,795,141 Β· updates every 60s
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