XPM Prime Explorer symbol
XPMPrime Explorer

Block #74,260

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 10:10:42 AM Β· Difficulty 8.9954 Β· 6,735,921 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8860b332b23a62098c5d6e38cd8378fcbe5db49cb7aac8ee6b2e8cbe2b1c3f9
View on Chainz β†—

Height

#74,260

Difficulty

8.995392

Transactions

1

Size

198 B

Version

2

Bits

08fed1fe

Nonce

119

Timestamp

7/21/2013, 10:10:42 AM

Confirmations

6,735,921

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

2ca191bf668092a91f094db023c127040923c7d9250cfd00ca8a10b780eaf1fd
Transactions (1)
Coinbase2ca191bf668092…8a10b780eaf1fd
1 in β†’ 1 out12.3400 XPM110 B
AZDgU5ry…dmcwdqVC
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.

1.614 Γ— 10⁹⁰(91-digit number)
16149060591157906769…99632422322986862319
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
1.614 Γ— 10⁹⁰(91-digit number)
16149060591157906769…99632422322986862319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.614 Γ— 10⁹⁰(91-digit number)
16149060591157906769…99632422322986862321
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
3.229 Γ— 10⁹⁰(91-digit number)
32298121182315813539…99264844645973724639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.229 Γ— 10⁹⁰(91-digit number)
32298121182315813539…99264844645973724641
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
6.459 Γ— 10⁹⁰(91-digit number)
64596242364631627078…98529689291947449279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.459 Γ— 10⁹⁰(91-digit number)
64596242364631627078…98529689291947449281
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
1.291 Γ— 10⁹¹(92-digit number)
12919248472926325415…97059378583894898559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.291 Γ— 10⁹¹(92-digit number)
12919248472926325415…97059378583894898561
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
2.583 Γ— 10⁹¹(92-digit number)
25838496945852650831…94118757167789797119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,725,517 XPMΒ·at block #6,810,180 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

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy