XPM Prime Explorer symbol
XPMPrime Explorer

Block #41,190

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 4:14:37 PM Β· Difficulty 8.5030 Β· 6,762,429 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ccb21a97a01d5ff928bc4f93dffc533660b18dbb75cadbef9518d4961e0dd5d7
View on Chainz β†—

Height

#41,190

Difficulty

8.502986

Transactions

2

Size

360 B

Version

2

Bits

0880c3ad

Nonce

161

Timestamp

7/14/2013, 4:14:37 PM

Confirmations

6,762,429

Mined by

⛏️ P2SHAVzQ3NvcgEu72cQUAUtfvzgK4M3tozGjpc

Merkle Root

e0f5ee302ba2e4030c0b9e42c83a78e3634d461258732a74c3a02849173d5d51
Transactions (2)
Coinbased3b86393672873…9381568b7f6cc2
1 in β†’ 1 out13.8200 XPM110 B
AVzQ3Nvc…3tozGjpc
66cdd874a14b2b…54ac5e49055a20
1 in β†’ 1 out15.6100 XPM159 B
Ad4tU5FR…YoLG8ved
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.

4.743 Γ— 10⁹⁢(97-digit number)
47434051136411220963…77714688155265061529
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
4.743 Γ— 10⁹⁢(97-digit number)
47434051136411220963…77714688155265061529
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.743 Γ— 10⁹⁢(97-digit number)
47434051136411220963…77714688155265061531
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
9.486 Γ— 10⁹⁢(97-digit number)
94868102272822441927…55429376310530123059
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.486 Γ— 10⁹⁢(97-digit number)
94868102272822441927…55429376310530123061
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
1.897 Γ— 10⁹⁷(98-digit number)
18973620454564488385…10858752621060246119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.897 Γ— 10⁹⁷(98-digit number)
18973620454564488385…10858752621060246121
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
3.794 Γ— 10⁹⁷(98-digit number)
37947240909128976770…21717505242120492239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.794 Γ— 10⁹⁷(98-digit number)
37947240909128976770…21717505242120492241
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:57,672,982 XPMΒ·at block #6,803,618 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