XPM Prime Explorer symbol
XPMPrime Explorer

Block #26,884

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 6:54:38 AM Β· Difficulty 7.9769 Β· 6,769,066 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5e78080ed015612380be0eb1713bc37c988d8a0f6efaff44c460d838405b9c1c
View on Chainz β†—

Height

#26,884

Difficulty

7.976870

Transactions

1

Size

198 B

Version

2

Bits

07fa1422

Nonce

105

Timestamp

7/13/2013, 6:54:38 AM

Confirmations

6,769,066

Mined by

⛏️ P2SHAbkSmUxWe8CpM5x3Luu7TZFAhJkwZbeu5a

Merkle Root

ba3ea15157b8f7e1eae096481755d70d13293f701f0652485ccccd36f31a8e8d
Transactions (1)
Coinbaseba3ea15157b8f7…cccd36f31a8e8d
1 in β†’ 1 out15.7000 XPM108 B
AbkSmUxW…kwZbeu5a
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.

4.753 Γ— 10⁹⁴(95-digit number)
47532441735241442371…83824502374277773279
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
4.753 Γ— 10⁹⁴(95-digit number)
47532441735241442371…83824502374277773279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.753 Γ— 10⁹⁴(95-digit number)
47532441735241442371…83824502374277773281
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
9.506 Γ— 10⁹⁴(95-digit number)
95064883470482884742…67649004748555546559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.506 Γ— 10⁹⁴(95-digit number)
95064883470482884742…67649004748555546561
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
1.901 Γ— 10⁹⁡(96-digit number)
19012976694096576948…35298009497111093119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.901 Γ— 10⁹⁡(96-digit number)
19012976694096576948…35298009497111093121
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
3.802 Γ— 10⁹⁡(96-digit number)
38025953388193153897…70596018994222186239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.802 Γ— 10⁹⁡(96-digit number)
38025953388193153897…70596018994222186241
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:57,611,689 XPMΒ·at block #6,795,949 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK