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Block #31,848

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 12:55:50 AM Β· Difficulty 7.9894 Β· 6,779,863 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7b00045e1ebad830dd6324719a92a2045f7bebd5cac1621aa8d601b4033d4091
View on Chainz β†—

Height

#31,848

Difficulty

7.989398

Transactions

1

Size

197 B

Version

2

Bits

07fd4938

Nonce

16

Timestamp

7/14/2013, 12:55:50 AM

Confirmations

6,779,863

Mined by

⛏️ P2SHAJbz55M2Xd4eSVXFrry1sb6y1EmoHxsz79

Merkle Root

5cb7d2ea6bd56ca3bc828318703b1659a527de064db79f3d84bbede2e639d250
Transactions (1)
Coinbase5cb7d2ea6bd56c…bbede2e639d250
1 in β†’ 1 out15.6500 XPM109 B
AJbz55M2…moHxsz79
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.

9.146 Γ— 10⁸⁹(90-digit number)
91469405902679136563…99554112779728751749
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
9.146 Γ— 10⁸⁹(90-digit number)
91469405902679136563…99554112779728751749
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.146 Γ— 10⁸⁹(90-digit number)
91469405902679136563…99554112779728751751
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
1.829 Γ— 10⁹⁰(91-digit number)
18293881180535827312…99108225559457503499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.829 Γ— 10⁹⁰(91-digit number)
18293881180535827312…99108225559457503501
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
3.658 Γ— 10⁹⁰(91-digit number)
36587762361071654625…98216451118915006999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.658 Γ— 10⁹⁰(91-digit number)
36587762361071654625…98216451118915007001
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
7.317 Γ— 10⁹⁰(91-digit number)
73175524722143309250…96432902237830013999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.317 Γ— 10⁹⁰(91-digit number)
73175524722143309250…96432902237830014001
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:57,737,800 XPMΒ·at block #6,811,710 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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