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Block #2,460,502

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/6/2018, 5:59:25 PM Β· Difficulty 10.9546 Β· 4,354,423 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0fc02eddaf339863d82d0ff40edeb647d385434040bdfb7f32889eb3fdb887b1
View on Chainz β†—

Height

#2,460,502

Difficulty

10.954579

Transactions

2

Size

724 B

Version

2

Bits

0af45f46

Nonce

1,033,942,212

Timestamp

1/6/2018, 5:59:25 PM

Confirmations

4,354,423

Mined by

⛏️ P2SHAKMm71Uum6EgpyKziih3raoZETx6JiGPit

Merkle Root

8c819413d408684beaa4b3762ff92c9be0c0e72f38353dc1ad36592b347780b3
Transactions (2)
Coinbase136ff760189959…3b9218aa5c6035
1 in β†’ 1 out8.3300 XPM110 B
AKMm71Uu…x6JiGPit
3a5e810707595e…5ac954ddbf86dc
3 in β†’ 2 out554.0087 XPM523 B
AT19qpdN…8DenzXz6AJ1wcjJw…dSLbnwjT
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.

1.271 Γ— 10⁹⁢(97-digit number)
12719400862894096978…39611871263238553599
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
1.271 Γ— 10⁹⁢(97-digit number)
12719400862894096978…39611871263238553599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.271 Γ— 10⁹⁢(97-digit number)
12719400862894096978…39611871263238553601
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
2.543 Γ— 10⁹⁢(97-digit number)
25438801725788193956…79223742526477107199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.543 Γ— 10⁹⁢(97-digit number)
25438801725788193956…79223742526477107201
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
5.087 Γ— 10⁹⁢(97-digit number)
50877603451576387912…58447485052954214399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.087 Γ— 10⁹⁢(97-digit number)
50877603451576387912…58447485052954214401
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
1.017 Γ— 10⁹⁷(98-digit number)
10175520690315277582…16894970105908428799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.017 Γ— 10⁹⁷(98-digit number)
10175520690315277582…16894970105908428801
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
2.035 Γ— 10⁹⁷(98-digit number)
20351041380630555164…33789940211816857599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.035 Γ— 10⁹⁷(98-digit number)
20351041380630555164…33789940211816857601
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:57,763,494 XPMΒ·at block #6,814,924 Β· updates every 60s
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