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Block #11,258

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/11/2013, 6:00:18 AM Β· Difficulty 7.7109 Β· 6,815,456 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0cb4d49a8dc51d81a1c78fbad976d1cdf9040c467eba423cc894046d1146daa4
View on Chainz β†—

Height

#11,258

Difficulty

7.710921

Transactions

1

Size

198 B

Version

2

Bits

07b5feef

Nonce

521

Timestamp

7/11/2013, 6:00:18 AM

Confirmations

6,815,456

Mined by

⛏️ P2SHATdcg5aGsKSGVEp9Y9eFvZwDgeu44DE6Kp

Merkle Root

198a282b0b07970f2cf371577769e2f1f635322eaa8ef8f1d8bf15ce4a63bf00
Transactions (1)
Coinbase198a282b0b0797…bf15ce4a63bf00
1 in β†’ 1 out16.8000 XPM109 B
ATdcg5aG…u44DE6Kp
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.

8.782 Γ— 10⁹¹(92-digit number)
87828871484190949812…88929627523207570899
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
8.782 Γ— 10⁹¹(92-digit number)
87828871484190949812…88929627523207570899
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.782 Γ— 10⁹¹(92-digit number)
87828871484190949812…88929627523207570901
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
1.756 Γ— 10⁹²(93-digit number)
17565774296838189962…77859255046415141799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.756 Γ— 10⁹²(93-digit number)
17565774296838189962…77859255046415141801
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
3.513 Γ— 10⁹²(93-digit number)
35131548593676379924…55718510092830283599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.513 Γ— 10⁹²(93-digit number)
35131548593676379924…55718510092830283601
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
7.026 Γ— 10⁹²(93-digit number)
70263097187352759849…11437020185660567199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.026 Γ— 10⁹²(93-digit number)
70263097187352759849…11437020185660567201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,857,865 XPMΒ·at block #6,826,713 Β· updates every 60s
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