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Block #35,523

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 8:12:11 AM Β· Difficulty 7.9945 Β· 6,774,053 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
77de08cd9b211e6e999baeeec2709b0d296989c46d534408e5709a1e03937891
View on Chainz β†—

Height

#35,523

Difficulty

7.994505

Transactions

2

Size

4.30 KB

Version

2

Bits

07fe97dc

Nonce

133

Timestamp

7/14/2013, 8:12:11 AM

Confirmations

6,774,053

Mined by

⛏️ P2SHAcK1grXGdn6sduvBHfrDuUhTPtn3ra4Sok

Merkle Root

d1bb9a8d1b8a8a1a62afe29387ebe340850a9b5069f8ceb50d1c1311a9cc6376
Transactions (2)
Coinbasefbd5a4fdb19e0e…24eba981c09e4b
1 in β†’ 1 out15.6800 XPM109 B
AcK1grXG…n3ra4Sok
abf6dd718f1770…57dc75ba62be60
35 in β†’ 2 out500.0500 XPM4.10 KB
AduwKP5J…wp1LyLxLAZ9fX4fu…aVfR43eV
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.

1.182 Γ— 10⁹⁴(95-digit number)
11822744883108493687…35336644772422507819
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
1.182 Γ— 10⁹⁴(95-digit number)
11822744883108493687…35336644772422507819
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.182 Γ— 10⁹⁴(95-digit number)
11822744883108493687…35336644772422507821
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
2.364 Γ— 10⁹⁴(95-digit number)
23645489766216987374…70673289544845015639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.364 Γ— 10⁹⁴(95-digit number)
23645489766216987374…70673289544845015641
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
4.729 Γ— 10⁹⁴(95-digit number)
47290979532433974748…41346579089690031279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.729 Γ— 10⁹⁴(95-digit number)
47290979532433974748…41346579089690031281
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
9.458 Γ— 10⁹⁴(95-digit number)
94581959064867949497…82693158179380062559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.458 Γ— 10⁹⁴(95-digit number)
94581959064867949497…82693158179380062561
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:57,720,685 XPMΒ·at block #6,809,575 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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