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Block #71,278

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2013, 5:52:15 PM Β· Difficulty 8.9930 Β· 6,724,785 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
29411042ab62c2dbd03245cfb41091c1666db96f4335339ea8254f0af22f2905
View on Chainz β†—

Height

#71,278

Difficulty

8.993033

Transactions

1

Size

201 B

Version

2

Bits

08fe3769

Nonce

238

Timestamp

7/20/2013, 5:52:15 PM

Confirmations

6,724,785

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

c46d095c748d25c158d1e0490f685e670ec7e8fd3641cf62afd3d56262ad6f95
Transactions (1)
Coinbasec46d095c748d25…d3d56262ad6f95
1 in β†’ 1 out12.3500 XPM110 B
AXSFye4r…ADf1YWCU
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.

2.410 Γ— 10⁹⁸(99-digit number)
24102303834976809597…41462434791536320399
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
2.410 Γ— 10⁹⁸(99-digit number)
24102303834976809597…41462434791536320399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.410 Γ— 10⁹⁸(99-digit number)
24102303834976809597…41462434791536320401
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
4.820 Γ— 10⁹⁸(99-digit number)
48204607669953619195…82924869583072640799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.820 Γ— 10⁹⁸(99-digit number)
48204607669953619195…82924869583072640801
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
9.640 Γ— 10⁹⁸(99-digit number)
96409215339907238391…65849739166145281599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.640 Γ— 10⁹⁸(99-digit number)
96409215339907238391…65849739166145281601
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
1.928 Γ— 10⁹⁹(100-digit number)
19281843067981447678…31699478332290563199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.928 Γ— 10⁹⁹(100-digit number)
19281843067981447678…31699478332290563201
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:57,612,598 XPMΒ·at block #6,796,062 Β· updates every 60s
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