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Block #1,428,717

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/26/2016, 9:16:31 AM Β· Difficulty 10.7429 Β· 5,408,210 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9bf03e22c3cb7017864b43e79d34b0d4ac2c0325f1fefcd349598131b7e076d9
View on Chainz β†—

Height

#1,428,717

Difficulty

10.742878

Transactions

2

Size

1.57 KB

Version

2

Bits

0abe2d45

Nonce

756,274,577

Timestamp

1/26/2016, 9:16:31 AM

Confirmations

5,408,210

Mined by

⛏️ P2SHAXUPwrjrwDm6ibfAzAZK7DDBBgs4HJPPHV

Merkle Root

f4df87deb1254fb8587c9c4b9677531793ae414c1a6752d26290792d957a69f1
Transactions (2)
Coinbase44263b2d232bc0…7cc9190b49b576
1 in β†’ 1 out8.6700 XPM109 B
AXUPwrjr…s4HJPPHV
1dddd0ac189e99…d364fd9b284f45
9 in β†’ 2 out1025.9500 XPM1.38 KB
AcDhjHA9…ebukETHzAYcRAB7N…AzRHf8fc
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.

2.477 Γ— 10⁹⁷(98-digit number)
24779258006049361389…13378742336252887039
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
2.477 Γ— 10⁹⁷(98-digit number)
24779258006049361389…13378742336252887039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.477 Γ— 10⁹⁷(98-digit number)
24779258006049361389…13378742336252887041
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
4.955 Γ— 10⁹⁷(98-digit number)
49558516012098722778…26757484672505774079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.955 Γ— 10⁹⁷(98-digit number)
49558516012098722778…26757484672505774081
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
9.911 Γ— 10⁹⁷(98-digit number)
99117032024197445556…53514969345011548159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.911 Γ— 10⁹⁷(98-digit number)
99117032024197445556…53514969345011548161
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
1.982 Γ— 10⁹⁸(99-digit number)
19823406404839489111…07029938690023096319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.982 Γ— 10⁹⁸(99-digit number)
19823406404839489111…07029938690023096321
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
3.964 Γ— 10⁹⁸(99-digit number)
39646812809678978222…14059877380046192639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.964 Γ— 10⁹⁸(99-digit number)
39646812809678978222…14059877380046192641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
7.929 Γ— 10⁹⁸(99-digit number)
79293625619357956445…28119754760092385279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,939,712 XPMΒ·at block #6,836,926 Β· updates every 60s
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