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Block #34,887

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 7:11:29 AM Β· Difficulty 7.9938 Β· 6,774,529 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00803a7086721d07c242b59992757415c8bcc0257c00a7517f689cb228c87fd4
View on Chainz β†—

Height

#34,887

Difficulty

7.993820

Transactions

1

Size

197 B

Version

2

Bits

07fe6afd

Nonce

5

Timestamp

7/14/2013, 7:11:29 AM

Confirmations

6,774,529

Mined by

⛏️ P2SHAV3Mx3AqCBr85EUqewYnyDKYAdAKiwER2W

Merkle Root

bec5ee2d7d1b2a6bc3fd4ef0b65ed9dca45f5afc301f715c0e6e0ee70b35ebea
Transactions (1)
Coinbasebec5ee2d7d1b2a…6e0ee70b35ebea
1 in β†’ 1 out15.6300 XPM109 B
AV3Mx3Aq…AKiwER2W
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.

6.833 Γ— 10⁸⁸(89-digit number)
68339556371755754166…82254688654147576609
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
6.833 Γ— 10⁸⁸(89-digit number)
68339556371755754166…82254688654147576609
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.833 Γ— 10⁸⁸(89-digit number)
68339556371755754166…82254688654147576611
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
1.366 Γ— 10⁸⁹(90-digit number)
13667911274351150833…64509377308295153219
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.366 Γ— 10⁸⁹(90-digit number)
13667911274351150833…64509377308295153221
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
2.733 Γ— 10⁸⁹(90-digit number)
27335822548702301666…29018754616590306439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.733 Γ— 10⁸⁹(90-digit number)
27335822548702301666…29018754616590306441
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
5.467 Γ— 10⁸⁹(90-digit number)
54671645097404603333…58037509233180612879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.467 Γ— 10⁸⁹(90-digit number)
54671645097404603333…58037509233180612881
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:57,719,396 XPMΒ·at block #6,809,415 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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