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Block #659,916

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/2/2014, 10:38:06 PM Β· Difficulty 10.9564 Β· 6,157,247 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bb5c59f9773c68c86ee40132473458d99b128702724e3a0b296c0cb6d14d82d5
View on Chainz β†—

Height

#659,916

Difficulty

10.956415

Transactions

2

Size

1.29 KB

Version

2

Bits

0af4d79c

Nonce

151,288,927

Timestamp

8/2/2014, 10:38:06 PM

Confirmations

6,157,247

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

31c12936b4f9d000fb0e8ba2a30282ee94231829c4b3f1f3cb875f9250a03741
Transactions (2)
Coinbase81ec2c18d43ba9…8d55d70c185073
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
a23242480b7c59…489ecd7635d2b6
7 in β†’ 2 out28.9580 XPM1.09 KB
Aby7bbmV…e5FRYgGcAPgeEFGV…Mi9CLSBE
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.

5.734 Γ— 10⁹⁢(97-digit number)
57340836720516122512…85497058472165906399
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
5.734 Γ— 10⁹⁢(97-digit number)
57340836720516122512…85497058472165906399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.734 Γ— 10⁹⁢(97-digit number)
57340836720516122512…85497058472165906401
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
1.146 Γ— 10⁹⁷(98-digit number)
11468167344103224502…70994116944331812799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.146 Γ— 10⁹⁷(98-digit number)
11468167344103224502…70994116944331812801
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
2.293 Γ— 10⁹⁷(98-digit number)
22936334688206449005…41988233888663625599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.293 Γ— 10⁹⁷(98-digit number)
22936334688206449005…41988233888663625601
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
4.587 Γ— 10⁹⁷(98-digit number)
45872669376412898010…83976467777327251199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.587 Γ— 10⁹⁷(98-digit number)
45872669376412898010…83976467777327251201
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
9.174 Γ— 10⁹⁷(98-digit number)
91745338752825796020…67952935554654502399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.174 Γ— 10⁹⁷(98-digit number)
91745338752825796020…67952935554654502401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.834 Γ— 10⁹⁸(99-digit number)
18349067750565159204…35905871109309004799
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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
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