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Block #11,031

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/11/2013, 5:14:05 AM Β· Difficulty 7.7004 Β· 6,784,657 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
18b125823961461da5f4af613212ecef70de5db6233d8caa4d349f7a0bd773cf
View on Chainz β†—

Height

#11,031

Difficulty

7.700360

Transactions

1

Size

201 B

Version

2

Bits

07b34ad2

Nonce

66

Timestamp

7/11/2013, 5:14:05 AM

Confirmations

6,784,657

Mined by

⛏️ P2SHAXsUn32ZVQMrvDLQGU6H7fn3xFJyQC98ip

Merkle Root

53cf8e0786a4b2cab0fa4ea6f36dda0ef03e88bad75bf4abcaaa6e0b80b44abd
Transactions (1)
Coinbase53cf8e0786a4b2…aa6e0b80b44abd
1 in β†’ 1 out16.8400 XPM109 B
AXsUn32Z…JyQC98ip
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.

1.119 Γ— 10¹⁰⁰(101-digit number)
11199787984418558414…71805796572785677469
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
1.119 Γ— 10¹⁰⁰(101-digit number)
11199787984418558414…71805796572785677469
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.119 Γ— 10¹⁰⁰(101-digit number)
11199787984418558414…71805796572785677471
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
2.239 Γ— 10¹⁰⁰(101-digit number)
22399575968837116829…43611593145571354939
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.239 Γ— 10¹⁰⁰(101-digit number)
22399575968837116829…43611593145571354941
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
4.479 Γ— 10¹⁰⁰(101-digit number)
44799151937674233659…87223186291142709879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.479 Γ— 10¹⁰⁰(101-digit number)
44799151937674233659…87223186291142709881
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
8.959 Γ— 10¹⁰⁰(101-digit number)
89598303875348467319…74446372582285419759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,609,573 XPMΒ·at block #6,795,687 Β· updates every 60s
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