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Block #272,515

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/25/2013, 7:21:47 AM Β· Difficulty 9.9530 Β· 6,536,050 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
441072700aa9963cf810f5bfdf1240b5fde764cfd0c7c092181497a33a47aad1
View on Chainz β†—

Height

#272,515

Difficulty

9.953030

Transactions

1

Size

200 B

Version

2

Bits

09f3f9cc

Nonce

55,459

Timestamp

11/25/2013, 7:21:47 AM

Confirmations

6,536,050

Mined by

⛏️ P2SHAcecj4WYP2kTRjXJMUTPed41WTwKtCNbS5

Merkle Root

410671bfda15577743cc6e0c9e97a99ec5be555c635d4a8285ad985887a41d70
Transactions (1)
Coinbase410671bfda1557…ad985887a41d70
1 in β†’ 1 out10.0800 XPM109 B
Acecj4WY…wKtCNbS5
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.

8.299 Γ— 10⁹⁢(97-digit number)
82992495168788049851…63160486709462526969
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
8.299 Γ— 10⁹⁢(97-digit number)
82992495168788049851…63160486709462526969
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.299 Γ— 10⁹⁢(97-digit number)
82992495168788049851…63160486709462526971
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
1.659 Γ— 10⁹⁷(98-digit number)
16598499033757609970…26320973418925053939
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.659 Γ— 10⁹⁷(98-digit number)
16598499033757609970…26320973418925053941
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
3.319 Γ— 10⁹⁷(98-digit number)
33196998067515219940…52641946837850107879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.319 Γ— 10⁹⁷(98-digit number)
33196998067515219940…52641946837850107881
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
6.639 Γ— 10⁹⁷(98-digit number)
66393996135030439881…05283893675700215759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.639 Γ— 10⁹⁷(98-digit number)
66393996135030439881…05283893675700215761
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
1.327 Γ— 10⁹⁸(99-digit number)
13278799227006087976…10567787351400431519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.327 Γ— 10⁹⁸(99-digit number)
13278799227006087976…10567787351400431521
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:57,712,578 XPMΒ·at block #6,808,564 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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