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Block #715,446

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2014, 8:01:32 PM Β· Difficulty 10.9542 Β· 6,089,521 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b130375766467a4ee8eb2427c8ad04c1cb0ac41bab7530a16c24ced95501a4ca
View on Chainz β†—

Height

#715,446

Difficulty

10.954180

Transactions

2

Size

993 B

Version

2

Bits

0af44525

Nonce

179,712,591

Timestamp

9/10/2014, 8:01:32 PM

Confirmations

6,089,521

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6a15891e187637bf5560f7ee7789da33764563d4218f0b372217f0912b038706
Transactions (2)
Coinbase2a2d52ec384b48…271d5e99898948
1 in β†’ 1 out8.3333 XPM116 B
ANSXnLY2…Sd25TjkD
2bb252cab8dca2…d550a9404a359c
5 in β†’ 1 out8.5300 XPM786 B
ARV7ntob…QKAQxrtv
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.

5.635 Γ— 10⁹⁢(97-digit number)
56351630508478059792…93518022126324273919
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
5.635 Γ— 10⁹⁢(97-digit number)
56351630508478059792…93518022126324273919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.635 Γ— 10⁹⁢(97-digit number)
56351630508478059792…93518022126324273921
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
1.127 Γ— 10⁹⁷(98-digit number)
11270326101695611958…87036044252648547839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.127 Γ— 10⁹⁷(98-digit number)
11270326101695611958…87036044252648547841
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
2.254 Γ— 10⁹⁷(98-digit number)
22540652203391223916…74072088505297095679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.254 Γ— 10⁹⁷(98-digit number)
22540652203391223916…74072088505297095681
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
4.508 Γ— 10⁹⁷(98-digit number)
45081304406782447833…48144177010594191359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.508 Γ— 10⁹⁷(98-digit number)
45081304406782447833…48144177010594191361
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
9.016 Γ— 10⁹⁷(98-digit number)
90162608813564895667…96288354021188382719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.016 Γ— 10⁹⁷(98-digit number)
90162608813564895667…96288354021188382721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,683,804 XPMΒ·at block #6,804,966 Β· updates every 60s
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