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Block #35,800

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 8:35:24 AM Β· Difficulty 7.9948 Β· 6,760,263 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c5e96dad1c3af27bfe32fd7f8247b948fddea7a162c1d280d519cedacf7234f5
View on Chainz β†—

Height

#35,800

Difficulty

7.994783

Transactions

1

Size

198 B

Version

2

Bits

07feaa13

Nonce

208

Timestamp

7/14/2013, 8:35:24 AM

Confirmations

6,760,263

Mined by

⛏️ P2SHALsDsAZMsUzVz3DPmszGZHGdXmEV8LNs7T

Merkle Root

f345d62dbfd3df9073414503c8390f5903138785bff34d7c105385c38714a002
Transactions (1)
Coinbasef345d62dbfd3df…5385c38714a002
1 in β†’ 1 out15.6200 XPM109 B
ALsDsAZM…EV8LNs7T
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.

8.071 Γ— 10⁹¹(92-digit number)
80712310362577304179…64789215074477608159
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
8.071 Γ— 10⁹¹(92-digit number)
80712310362577304179…64789215074477608159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.071 Γ— 10⁹¹(92-digit number)
80712310362577304179…64789215074477608161
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
1.614 Γ— 10⁹²(93-digit number)
16142462072515460835…29578430148955216319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.614 Γ— 10⁹²(93-digit number)
16142462072515460835…29578430148955216321
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
3.228 Γ— 10⁹²(93-digit number)
32284924145030921671…59156860297910432639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.228 Γ— 10⁹²(93-digit number)
32284924145030921671…59156860297910432641
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
6.456 Γ— 10⁹²(93-digit number)
64569848290061843343…18313720595820865279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.456 Γ— 10⁹²(93-digit number)
64569848290061843343…18313720595820865281
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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