XPM Prime Explorer symbol
XPMPrime Explorer

Block #253,083

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/9/2013, 10:44:23 PM Β· Difficulty 9.9718 Β· 6,543,203 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c370b63ef65f3a3436586159c85d000f2751cddf14c3bb181ab1d459d3aef1df
View on Chainz β†—

Height

#253,083

Difficulty

9.971839

Transactions

1

Size

209 B

Version

2

Bits

09f8ca70

Nonce

134,218,299

Timestamp

11/9/2013, 10:44:23 PM

Confirmations

6,543,203

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

6a771f675cf3995e43efdfc62ad5c2dcb9ca63cfa364f61f78bc2b5a57eb8b86
Transactions (1)
Coinbase6a771f675cf399…bc2b5a57eb8b86
1 in β†’ 1 out10.0400 XPM116 B
AcLBm5Z9…S683d7c3
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.

8.835 Γ— 10¹⁰²(103-digit number)
88354648933405049853…35529946784282519799
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
8.835 Γ— 10¹⁰²(103-digit number)
88354648933405049853…35529946784282519799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.835 Γ— 10¹⁰²(103-digit number)
88354648933405049853…35529946784282519801
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
1.767 Γ— 10¹⁰³(104-digit number)
17670929786681009970…71059893568565039599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.767 Γ— 10¹⁰³(104-digit number)
17670929786681009970…71059893568565039601
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
3.534 Γ— 10¹⁰³(104-digit number)
35341859573362019941…42119787137130079199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.534 Γ— 10¹⁰³(104-digit number)
35341859573362019941…42119787137130079201
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
7.068 Γ— 10¹⁰³(104-digit number)
70683719146724039882…84239574274260158399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.068 Γ— 10¹⁰³(104-digit number)
70683719146724039882…84239574274260158401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.413 Γ— 10¹⁰⁴(105-digit number)
14136743829344807976…68479148548520316799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.413 Γ— 10¹⁰⁴(105-digit number)
14136743829344807976…68479148548520316801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,614,291 XPMΒ·at block #6,796,285 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